Abstract Non-reductive physicalism is currently the most widely held metaphysic of mind. My aim in this essay is to show that supervenience physicalism?perhaps the most common form of non-reductive physicalism?is not a defensible position. I argue that, in order for any supervenience thesis to ground a legitimate form of physicalism, it must yield the right sort of determination relation between physical and non-physical properties. Then I argue that non-reductionism leaves one without any explanation for the laws that are implied by (...) supervenience theses that deliver this determination relation. (shrink)